Question

What relative masses of dimethyl amine and dimethyl ammonium chloride do you need to prepare a buffer solution of pH = 10.58?

units of answer should be: g of(CH3)2NH per 1g (CH3)2NH2Cl

Answer 1

For dimethylamine:
Acidity (pKa) 10.64
Basicity (pKb) 3.36

At this point have a short think: If the molar ratio of dimethylamine : dimethylammonium chloride was 1 :1 you would be at the half equivalence point , and pH would equal pKa . The pH would be 10.64.
But you want a buffer with pH = 10.58. Therefore there must be a molar excess of the dimethylammonium chloride.

Use the H-H equation:
pH = pKa + log ( [[base]/[salt]]
10.58 = 10.64 + log ([base[/[salt])
log ([base[/]salt]) = 10.58 - 10.64
log ([base]/[salt] = -0.06
[base]/[salt] = 10^-0.06
[base]/[salt] = 0.8709

The buffer must be prepared by mixing 0.8709mol dimethylamine and 1.0mol dimethylammonium chloride.
Mass ratio as required:
Molar mass dimethylammonium chloride 81.55g/mol
Molar mass dimethylamine = 45.08g/mol - 0.8709 mol = 39.26 g

Mass ratio of dimethylammonium chloride : dimethylamine = 81.55 : 39.26

OR Ratio = 81.55/39.26 = 2.077 :1